SAUSALITO MARIN CITY SCHOOL DISTRICT
Mathematics Standards - GRADE 4
By the end of fourth grade, students understand large numbers
and addition, subtraction, multiplication and division of whole
numbers. They describe and compare simple fractions and
decimals. They understand the properties of and the
relationships between plane geometric figures. They collect,
represent and analyze data to answer questions.
NUMBER SENSE
1. Students understand place value of whole numbers and
decimals to two decimal places, how these relate to simple
fractions, and use concepts of negative numbers.
+1.1. read and write whole numbers in the millions
+1.2. order and compare whole numbers and
decimals to two decimal places
+1.3. round whole numbers through the millions to
the nearest ten, hundred, thousand, ten thousand or
hundred thousand
+1.4. decide when a rounded solution is called for,
and explain why this is the case
1.5. interpret different meanings for fractions
including parts of a whole, parts of a set, indicate
division of whole numbers and quantities (and
measures) between whole numbers on a number line;
and relate to simple decimals on a number line
(1) use manipulatives to compare whole
numbers and fractions
(2) connect manipulatives to numeric
notation in order to describe and
compare whole numbers and fractions
1.6. write tenths and hundredths in decimal and
fraction notation and know fraction/decimal
equivalents for halves and fourths (e.g., 1/2 = 0.5 or
.50; 7/4 = 1 3/4 = 1.75)
1.7. write the fraction represented by a drawing of
parts of a figure; represent a given fraction using
drawings
(1) use pictorial and concrete models to
show relationships
+1.8. use concepts of negative numbers (e.g., on a
number line, in counting, in temperature, "owing")
+1.9. identify the relative position of fractions, mixed
numbers, and decimals to two decimal places on the
number line
2. Students extend their use and understanding of whole
numbers to addition and subtraction of simple decimals.
2.1. estimate and compute the sum or difference of
whole numbers and positive decimals to two places
(1) add and subtract money and make
change
2.2. round two place decimals to one decimal or the
nearest whole number, and use rounding to judge the
reasonableness of an answer
2.3. write and solve real world problems using
addition and subtraction
+3. Students solve problems involving addition, subtraction,
multiplication and division of whole numbers, including
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the addition and subtraction of negative numbers, and
understand the relationships among the operations.
+3.1. demonstrate understanding of, and the ability to
use standard algorithms for addition and subtraction
of multi-digit numbers
+3.2. demonstrate understanding of, and ability to use
standard algorithms for multiplying a multi-digit
number by a two digit number and long division for
dividing a multi-digit number by a one digit number;
use relationships between them to simplify
computations and to check results
+3.3. solve problems involving multiplication of
multi-digit numbers by two-digit numbers
+3.4. solve problems involving division of multi-digit
numbers by one-digit numbers
3.5. understand division in real life situations as
either sharing or grouping
3.6. understand how to interpret the quotient and
remainder to solve real life situations
4. Students know how to factor small whole numbers.
4.1. understand that many whole numbers
decompose in different ways (e.g., 12 = 4 x 3 = 2 x 6
= 2 x 2 x 3)
+4.2. know that numbers such as 2, 3, 5, 7, 11 do not
have any factors except 1 and themselves, and that
such numbers are called prime numbers
ALGEBRA AND FUNCTIONS
1. Students use and interpret variables, mathematical
symbols and properties to write and simplify expressions
and sentences.
1.1. describe, analyze and create a wide variety of
patterns and relationships (e.g., geometric and
numeric)
1.2. use letters, boxes, or other symbols to stand for
any number in simple expressions or equations (e.g.,
demonstrate understanding and use of a concept of a
variable)
+1.3. interpret and evaluate mathematical expressions
that use parentheses
+1.4. use parentheses to indicate which operation to
perform first when writing expressions containing
more than two terms and different operations
1.5. use and interpret formulas (e.g., Area = length
times width or A = lw) to answer
questions about quantities and their relationships
+1.6. understand that an equation such as y = 3x + 5
is a prescription for determining a second number
when a first number is given
+2. Students know how to manipulate equations.
+2.1. know and understand that equals added to
equals are equal
+2.2. know and understand that equals multiplied by
equals are equal
MEASUREMENT AND GEOMETRY
1. Students understand perimeter and area.
1.1. select and use appropriate units for
Grade 4 – Pg. 1
measuring
1.2. measure the area of rectangular shapes, using
appropriate units: square centimeter, square meter,
square kilometer, square inches, square yard, square
mile
1.3. recognize that the rectangles having the same
area can have different perimeters
1.4. understands that rectangles that have the same
perimeter can have different areas.
1.5. understand and use formulas to solve problems
involving perimeters and areas of rectangles and
squares. Use these formulas to find the areas of more
complex figures by
dividing them into parts with these basic shapes
+2. Students use two-dimensional coordinate grids to
represent points and graph lines and simple figures.
+2.1. draw the points corresponding to linear
relationships on graph paper (e.g., draw the first ten
points for the equation y = 3x and connect them using
a straight line)
+2.2. understand that the length of a horizontal line
segment equals the difference of the x-coordinates
+2.3. understand that the length of a vertical line
segment equals the difference of the y-coordinates
3. Students demonstrate understanding of plane and solid
geometric objects. They use this knowledge to show
relationships and solve problems.
3.1. identify lines that are parallel and perpendicular
3.2. identify the radius and diameter of a circle
3.3. identify congruent figures
3.4. identify figures that have bilateral and rotational
symmetry
3.5. know the definitions of right angle, acute angle
and obtuse angle; understand that 90, 180, 270, and
360 degrees are, respectively, associated with 1/4,
1/2, 3/4 and full turns.
3.6. visualize, describe and represent geometric solids
(e.g., prisms, pyramids, etc.) in terms of the number
and shape of faces, edges and
vertices; interpret two-dimensional representations of
three-dimensional objects; and draw patterns (of
faces) for a solid that when folded will make a model
of the solid
3.7. know the definitions of different triangles (e.g.,
equilateral, isosceles, scalene) and identify their
features
3.8. know the definition of different
quadrilaterals (e.g., rhombus, square, rectangle,
parallelogram, trapezoid)
STATISTICS, DATA ANALYSIS and PROBABILITY
1. Students organize, represent and interpret numerical and
categorical data, and clearly communicate their findings.
1.4. interpret one- and two-variable data graphs to
answer questions about a situation
2. Students make predictions for simple probability
situations.
2.1. represent all possible outcomes for a simple
probability situation in an organized way (e.g., tables,
grids, tree diagrams)
2.2. express outcomes of experimental
probability situations verbally and numerically (e.g.,
3 out of 4; 3/4)
MATHEMATICAL REASONING
1. Students make decisions about how to approach
problems.
1.1. analyze problems by identifying relationships,
discriminating relevant from irrelevant information,
sequencing and prioritizing information, and
observing patterns
1.2. determine when and how to break a problem into
simpler parts
1.3. explain decisions about the approaches,
materials, and strategies used to solve problems
2. Students use strategies, skills and concepts in finding
solutions.
2.1. use estimation to verify the reasonableness of
calculated results
2.2. apply strategies and results from simpler
problems to more complex problems
2.3. use a variety of methods such as words,
numbers, symbols, charts, graphs, tables, diagrams
and models to explain mathematical reasoning
2.4. express the solution clearly and logically using
appropriate mathematical notation and terms and
clear language; support solutions with evidence, in
both verbal and symbolic work
2.5. indicate the relative advantages of exact and
approximate solutions to problems and give
answers to a specified degree of accuracy
2.6. make precise calculations and check the
validity of the results from the context of the
problem
3. Students move beyond a particular problem by
generalizing to other situations.
3.1. evaluate the reasonableness of the solution in the
context of the original situation
3.2. note method of deriving the solution and
demonstrate conceptual understanding of the
derivation by solving similar problems
3.3. develop generalizations of the results obtained
and extend them to other circumstances
1.1. compare data in order to make true statements
and draw conclusions based on the data
1.2. formulate survey questions, systematically
collect and represent data on a number line,
coordinate graphs, tables and charts
1.3. identify the mode(s) for sets of categorical data,
and the mode(s), median, and any
apparent outliers for numerical data sets
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Grade 4 – Pg. 2